XTREMES amply meets its primary aim to aid the teaching of ideas about extreme value analysis. It would be attractive to use (perhaps with computer-linked overhead projection facilities) to illustrate lectures on both theoretical and practical topics in a course on statistical extremes. The simulation facility described in S3.4 could be used also to illustrate lectures on robustness. Students would benefit also from working with the package individually on practical problems, since this would consolidate their understanding of concepts, and foster the important exploratory and empirical attitude to statistical analysis referred to in S3.3. The manual Hassmann et al (1993) in fact contains practical exercises and examples for a laboratory course.
The package is also, as its authors hoped, likely to be of some use in the practitioner's analysis or real extreme value problems, especially if the data can be assumed homogeneous. Provision of standard errors for the calculated point estimates would be welcome in this context though, and some means of attaching a measure of precision to estimates of future high quantiles of the variable under study. Likelihood methods could meet this need, and so there is a case for their inclusion amongst the armoury of provided techniques. The estimation facilities in the package are at present limited to homogeneous samples. Yet in many real problems observations may depend to some extent on external influences which will often be quantifiable, at least approximately. Human longevity, for example, could well be changing with time, influenced by economic well-being and medical progress. It is desirable therefore that an analysis of such data should allow for the possibility of inhomogeneity, and should offer some means of modelling and testing it. Models which can incorporate covariate information could do this, and together with associated inference procedures would offer an extremely powerful extension of XTREMES' capabilities. A further extension would be the introduction of multivariate techniques. On the evidence of Falk et al (1994) the authors already have in mind some of these possibilities for future versions.
In summary, XTREMES succeeds resoundingly in its primary didactic aim, and makes a worthwhile first step in the provision of tools for extreme value practitioners. It deserves a warm welcome, not only for what it offers already, but also because of its potential as a springboard for further development.
REFERENCES
Falk, M., Hüsler, J. and Reiss, R.-D. (1994) Laws of Small Numbers:
Extremes and Rare Events, DMV-Seminar: Bd 23, Birkhäuser Verlag, Basel,
Boston, Berlin.
Hassmann, S., Reiss, R.-D. and Thomas, M. (1993) XTREMES: Extreme
Value Analysis and Robustness, XTREMES Group, Siegen.